Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-08T16:33:40.976Z Has data issue: false hasContentIssue false
  • English
  • Français

Sensitivity of MRQAP Tests to Collinearity and Autocorrelation Conditions

Published online by Cambridge University Press:  01 January 2025

David Dekker ,
David Krackhardt  and
Tom A. B. Snijders
David Dekker*
Affiliation:
Radboud University Nijmegen
David Krackhardt
Affiliation:
Carnegie Mellon University
Tom A. B. Snijders
Affiliation:
University of Groningen and University of Oxford
*
Requests for reprints should be sent to David Dekker, Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000DR Rotterdam, The Netherlands. E-mail: ddekker@few.eur.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

Multiple regression quadratic assignment procedures (MRQAP) tests are permutation tests for multiple linear regression model coefficients for data organized in square matrices of relatedness among n objects. Such a data structure is typical in social network studies, where variables indicate some type of relation between a given set of actors. We present a new permutation method (called “double semi-partialing”, or DSP) that complements the family of extant approaches to MRQAP tests. We assess the statistical bias (type I error rate) and statistical power of the set of five methods, including DSP, across a variety of conditions of network autocorrelation, of spuriousness (size of confounder effect), and of skewness in the data. These conditions are explored across three assumed data distributions: normal, gamma, and negative binomial. We find that the Freedman–Lane method and the DSP method are the most robust against a wide array of these conditions. We also find that all five methods perform better if the test statistic is pivotal. Finally, we find limitations of usefulness for MRQAP tests: All tests degrade under simultaneous conditions of extreme skewness and high spuriousness for gamma and negative binomial distributions.

Keywords

MRQAPMantel testspermutation testssocial networksnetwork autocorrelationcollinearitydyadic data
Type
Theory and Methods
Information
Psychometrika , Volume 72 , Issue 4 , December 2007 , pp. 563 - 581
Copyright
Copyright © 2007 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Special thanks go to Cajo Ter Braak, Philip Hans Franses, Patrick Houweling, Pierre Legendre, three anonymous reviewers, the associate editor, and the editor for comments.

References

Anderson, M.J., Legendre, P. (1999). An empirical comparison of permutation methods for tests of partial regression coefficients in a linear model. Journal of Statistical Computation and Simulation, 62(3), 271–303.CrossRefGoogle Scholar
Anderson, M.J., Robinson, J. (2001). Permutation tests for linear models. Australian & New Zealand Journal of Statistics, 43(1), 75–88.CrossRefGoogle Scholar
Anderson, M.J., Ter Braak, C.J.F. (2003). Permutation tests for multi-factorial analysis of variance. Journal of Statistical Computation and Simulation, 73(2), 85–113.CrossRefGoogle Scholar
Baker, F., Hubert, L. (1981). The analysis of social interaction data. Sociological Methods and Research, 9, 339–361.CrossRefGoogle Scholar
Borgatti, S.P., Cross, R. (2003). A relational view of information seeking and learning in social networks. Management Science, 49(4), 432–445.CrossRefGoogle Scholar
Borgatti, S.P., Everett, M.G., Freeman, L.C. (2002). Ucinet for windows: Software for social network analysis, Boston: Harvard Analytic Technologies.Google Scholar
Edgington, E. (1995). Randomization tests, (3rd ed.). New York: Dekker.Google Scholar
Frank, O., Strauss, D. (1986). Markov graphs. Journal of the American Statistical Association, 81(395), 832–842.CrossRefGoogle Scholar
Freedman, D., Lane, D. (1983). A nonstochastic interpretation of reported significance levels. Journal of Business and Economic Statistics, 1, 292–298.CrossRefGoogle Scholar
Gibbons, D., Olk, P.M. (2003). Individual and structural origins of friendship and social position among professionals. Journal of Personality and Social Psychology, 84(2), 340–351.CrossRefGoogle ScholarPubMed
Heagerty, P.J., Lele, S.R. (1998). A composite likelihood approach to binary spatial data. Journal of the American Statistical Association, 93, 1099–1123.CrossRefGoogle Scholar
Holland, P.W., Leinhardt, S. (1981). An exponential family of probability-distributions for directed-graphs. Journal of the American Statistical Association, 76(373), 33–50.CrossRefGoogle Scholar
Hubert, L.J. (1987). Assignment methods in combinatorial data analysis, New York: Dekker.Google Scholar
Jackson, D.A., Somers, K.M. (1989). Are probability estimates from the permutation model of Mantel’s test stable?. Canadian Journal of Zoology, 67, 766–769.CrossRefGoogle Scholar
Kadushin, C. (1995). Friendships among the French financial elite. American Sociological Review, 60(2), 201–221.CrossRefGoogle Scholar
Kennedy, P.E. (1995). Randomization tests in econometrics. Journal of Business & Economic Statistics, 13(1), 85–94.CrossRefGoogle Scholar
Kennedy, P.E., Cade, B.S. (1996). Randomization tests for multiple regression. Communications in Statistics—Simulation and Computation, 25(4), 923–936.CrossRefGoogle Scholar
Krackhardt, D. (1987). Qap partialling as a test of spuriousness. Social Networks, 9, 171–186.CrossRefGoogle Scholar
Krackhardt, D. (1988). Predicting with networks—Nonparametric multiple-regression analysis of dyadic data. Social Networks, 10(4), 359–381.CrossRefGoogle Scholar
Krackhardt, D., Kilduff, M. (1990). Friendship patterns and culture: The control of organizational diversity. American Anthropologist, 92, 142–154.CrossRefGoogle Scholar
Krackhardt, D., Kilduff, M. (1999). Whether close or far: Perceptions of balance in friendship networks in organizations. Journal of Personality and Social Psychology, 76, 770–782.CrossRefGoogle Scholar
Krempel, L., & Plümper, T. (2003). Exploring the dynamics of international trade by combining the comparative advantages of multivariate statistics and network visualization. Journal of Social Structure, 4(1) (electronic).Google Scholar
Laumann, E.O., Marsden, P.V., Galaskiewicz, J. (1977). Community-elite influence structures: Extension of a network approach. American Journal of Sociology, 83(3), 594–631.CrossRefGoogle Scholar
Laumann, E.O., Pappi, F.U. (1976). Networks of collective action: A perspective on community influence systems, New York: Academic Press.Google Scholar
Legendre, P. (2000). Comparison of permutation methods for the partial correlation and partial Mantel tests. Journal of Statistical Computation and Simulation, 67(1), 37–73.CrossRefGoogle Scholar
Legendre, P., Anderson, M. (1999). Distance-based redundancy analysis: Testing multi-species responses in multi-factorial ecological experiments. Ecological Monographs, 69, 1–24.CrossRefGoogle Scholar
Legendre, P., Lapointe, F.-J., Casgrain, P. (1994). Modeling brain evolution from behavior: A permutational regression approach. Evolution, 48, 1487–1499.CrossRefGoogle ScholarPubMed
Manly, B. (1997). Randomization, bootstrap, and Monte Carlo methods in biology, (2nd ed.). London: Chapman & Hall.Google Scholar
Mantel, N. (1967). The detection of disease clustering and a generalized regression approach. Cancer Research, 27(2), 209–220.Google Scholar
Mizruchi, M.S. (1990). Capitalist collective action: Competition, cooperation, and conflict in the coal industry, by J.R. Bowman. American Journal of Sociology, 96(2), 473–475.CrossRefGoogle Scholar
Nelson, R.E. (1989). The strength of strong ties: Social networks and intergroup conflict in organizations. Academy of Management Journal, 32, 377–401.CrossRefGoogle Scholar
Oden, N.L., Sokal, R.R. (1992). An investigation of 3-matrix permutation tests. Journal of Classification, 9(2), 275–290.CrossRefGoogle Scholar
Oja, H. (1987). On permutation tests in multiple regression and analysis of covariance problems. Australian Journal of Statistics, 29, 81–100.CrossRefGoogle Scholar
Pattison, P.E. (1988). Network models: Some comments on papers in this special issue. Social Networks, 10(4), 383–411.CrossRefGoogle Scholar
Pitman, E. (1937). Significance tests which may be applied to samples from any population. Royal Statistical Society, Supplement, 4, 119–130.Google Scholar
Proctor, C.H. (1969). Analyzing pair data and point data on social relationships, attitudes and background characteristics of Costa Rican Census Bureau employees. Social Statistics Section, Proceedings of the American Statistical Association, pp. 457–465.Google Scholar
Smouse, P.E., Long, J.C., Sokal, R.R. (1986). Mutiple regression and correlation extensions of the Mantel test of matrix correspondence. Systematic Zoology, 35(4), 627–632.CrossRefGoogle Scholar
Snijders, T., Pattison, P., Robins, G., Handcock, M. (2006). New specifications for exponential random graph models. Sociological Methodology, 36, 99–153.CrossRefGoogle Scholar
Sorenson, O., Stuart, T.E. (2001). Syndication networks and the spatial distribution of venture capital investments. American Journal of Sociology, 106(6), 1546–1588.CrossRefGoogle Scholar
Stuart, A., Ord, J.K. (2005). Kendall’s advanced theory of statistics: Vol. 1, London: Arnold.Google Scholar
Ter Braak, C. (1992). Permutation versus bootstrap significance tests in multiple regression and ANOVA. In Jöckel, K.-H., Rothe, G., Sendler, W. (Eds.), Bootstrapping and related techniques, Berlin: Springer.Google Scholar
Wasserman, S., Pattison, P. (1996). Logit models and logistic regressions for social networks. 1. An introduction to Markov graphs and p *. Psychometrika, 61(3), 401–425.CrossRefGoogle Scholar
Welch, W. (1990). Construction of permutation tests. Journal of the American Statistical Association, 85, 693–698.CrossRefGoogle Scholar